Assyria and Syria are not the same thing. Syria was probably named after Assyria and Assyria once ruled Syria, but it wasn't the heartland of Assyria, it was just some territory. Syria is named after the Roman province of Syria, which is named after the Seleucid Syria, which is named after Assyria (more or less, iirc).
As for Syria. They were a French colony (Mandate) until 1946 and haven't really established much about themselves since. Their period prior to Baath rule was relatively unstable and there's not much to say. The brief United Arab Republic was interesting, but Egyptian dominated and, well, extremely brief.
Modern Syria is hard no matter what. Hafez al-Assad is probably the most logical choice. All their military is American and Soviet surplus. I don't think any of it was particularly unique. And they haven't had much time to establish themselves in any way.
If we're talking about historic Syria, there's the Aramaeans, who basically became merchants and traded all over the Middle East (to the point where their language became an international language). They ruled a powerful city of Damascus. There's the Seleucid Empire, which were a successor to Alexander the Great's Empire. Their Empire stretched all the way through Persia, but slowly lost territory. The remaining core was based around Antioch and was an interesting mix of Greek culture and traditional Mesopotamian culture. There's the Islamic Umayyad Empire, based in Damascus, but that might be better represented by the Arabs. Finally, there's the Crusader Kingdoms of Edessa and Antioch, who might be interesting.
I guess the question is what you're looking for. In my mind, all those groups I just mentioned are more interesting than modern Syria, but, if you're looking to represent modern Syria, they're not helpful. As a Ba'ath state, their institutions were military dominated and tend to parallel Iraqi ones (for example, "Republican Guard" is a logical choice for a unique unit for both except for the fact that it's obviously not unique). Unlike Iraq, they were able to continue to develop chemical weapons, so that's something that's unique to them. Aside from that, I can't really help.